Probably from Hackney, formerly a town, now a borough of London, used for grazing horses before sale, or from Old French haquenee (“ambling mare for ladies”), Latinized in England to hakeneius (though some recent French sources report that the English usage predates the French)

(in compounds) (A means of transportation that is) available for public hire.

Origin

The senses "a horse" and "(a means of transport) available for hire" derive from the fact that many horses were kept in the London borough of Hackney, and were available for hire. The place name is from Old English Hacanieg "Hacan's Isle" ("Hook's Island"), referring to dry land in a marsh.